Highest Common Factor of 665, 774, 130 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 665, 774, 130 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 665, 774, 130 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 665, 774, 130 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 665, 774, 130 is 1.
HCF(665, 774, 130) = 1
HCF of 665, 774, 130 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 665, 774, 130 is 1.
Highest Common Factor of 665,774,130 is 1
Step 1: Since 774 > 665, we apply the division lemma to 774 and 665, to get
774 = 665 x 1 + 109
Step 2: Since the reminder 665 ≠ 0, we apply division lemma to 109 and 665, to get
665 = 109 x 6 + 11
Step 3: We consider the new divisor 109 and the new remainder 11, and apply the division lemma to get
109 = 11 x 9 + 10
We consider the new divisor 11 and the new remainder 10,and apply the division lemma to get
11 = 10 x 1 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 665 and 774 is 1
Notice that 1 = HCF(10,1) = HCF(11,10) = HCF(109,11) = HCF(665,109) = HCF(774,665) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 130 > 1, we apply the division lemma to 130 and 1, to get
130 = 1 x 130 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 130 is 1
Notice that 1 = HCF(130,1) .
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Frequently Asked Questions on HCF of 665, 774, 130 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 665, 774, 130?
Answer: HCF of 665, 774, 130 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 665, 774, 130 using Euclid's Algorithm?
Answer: For arbitrary numbers 665, 774, 130 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
